AIXI is a theoretical model for a maximally intelligent hypothetical agent, developed by Marcus Hutter. As it is not computable--though computable variants exist--it does not serve not as a design for a real AI. But it is valuable as a theoretical model of intelligence, as it abstracts away resource limitations that limit the intelligence of and complicate the analysis of real-world AI. It works by simulating all possible actions into the future, considering simpler hypotheses about the way the world works as more likely,

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{{arbitallink|https://arbital.com/p/AIXI/|AIXI}}

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AIXI is a mathematical formalism for a hypothetical (super)intelligent agent, developed by Marcus Hutter (2005, 2007). AIXI is not computable, and so does not serve as a design for a real-world AI, but is considered a valuable theoretical illustration with both positive and negative aspects (things AIXI would be able to do and things it arguably couldn't do).

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The agent model in which AIXI operates is as follows: There is an *agent*, and an *environment*, which is a computable function unknown to the agent. So, the agent will need to have a probability distribution on the range of possible environments. On each clock tick, the agent receives an *observation* (a bitstring/number) from the environment, as well as a reward (another number). The agent then outputs an *action* (another number). Then again, on each iteration, the environment provides an observation and reward as a function of the full history of the interaction, and agent outputs its action likewise. The agent's intelligence is defined by its expected reward across all environments.

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The AIXI formalism says roughly to consider all possible computable models of the environment, Bayes-update them on past experiences, and use the resulting updated predictions to model the expected sensory reward of all possible strategies.

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AIXI guesses at a probability distribution for its environment using [[Solomonoff induction]], a formalization of [[Occam's razor]]: Simpler environments are considered to be more likely than more complex ones. It then calculates the expected reward of each action it might choose--weighting the possible environments as mentioned--and chooses the best action. It does this calculation by extrapolating its actions into the future recursively, using the assumption that at each step into the future it will again choose the best possible action using the same procedure.

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AIXI can be viewed as the border between AI problems that would be 'simple' to solve using unlimited computing power and problems which are structurally 'complicated'.

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AIXI is provably more intelligent than any other possible agent. However, it is not a feasible AI, as [[Solomonoff induction]] is not computable; and it evaluates expected value over an infinite set of possible actions on each iteration. However, it has served to inspire a computable variant, AIXItl. Given constraints on time and space, AIXItl is provably more intelligent than any other agent working within the same constraints. AIXItl too is intractable, but implementable variants such as the Monte Carlo approximation by Veness et al. have shown promising results in simple general-intelligence test problems.

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==How AIXI works==

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Hutter (2007) describes AIXI as a combination of decision theory and algorithmic information theory: "Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff’s theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameterless theory of universal Artificial Intelligence."

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[[Eliezer Yudkowsky]] has raised the [[Anvil problem]]. AIXI lacks a self-model: It extrapolates its own actions into the future indefinitely, on the assumption that it will keep working in the same way in the future. Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could change its behavior due to bugs; and the AIXI formalism completely ignores these possibilities.

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AIXI operates within the following agent model: There is an ''agent'', and an ''environment'', which is a computable function unknown to the agent. Thus the agent will need to have a probability distribution on the range of possible environments.

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On each clock tick, the agent receives an ''observation'' (a bitstring/number) from the environment, as well as a reward (another number).

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The agent then outputs an ''action'' (another number).

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To do this, AIXI guesses at a probability distribution for its environment, using [[Solomonoff induction]], a formalization of [[Occam's razor]]: Simpler computations are more likely ''a priori'' to describe the environment than more complex ones. This probability distribution is then Bayes-updated by how well each model fits the evidence (or more precisely, by throwing out all computations which have not exactly fit the environmental data so far, but for technical reasons this is roughly equivalent as a model). AIXI then calculates the expected reward of each action it might choose--weighting the likelihood of possible environments as mentioned. It chooses the best action by extrapolating its actions into its future time horizon recursively, using the assumption that at each step into the future it will again choose the best possible action using the same procedure.

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Then, on each iteration, the environment provides an observation and reward as a function of the full history of the interaction; the agent likewise is choosing its action as a function of the full history.

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The agent's intelligence is defined by its expected reward across all environments, weighting their likelihood by their complexity.

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AIXI it is not a feasible AI, because [[Solomonoff induction]] is not computable, and because some environments may not interact over finite time horizons (AIXI only works over some finite time horizon, though any finite horizon can be chosen). A somewhat more computable variant is the time-space-bounded AIXItl. Real AI algorithms explicitly inspired by AIXItl, e.g. the Monte Carlo approximation by Veness et al. (2011) have shown interesting results in simple general-intelligence test problems.

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For a short (half-page) technical introduction to AIXI, see [http://www.jair.org/media/3125/live-3125-5397-jair.pdf Veness et al. 2011], page 1-2. For a full exposition of AIXI, see [http://www.hutter1.net/ai/aixigentle.htm Hutter 2007].

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==Relevance to Friendly AI==

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Because it abstracts optimization power away from human mental features, AIXI is valuable in considering the possibilities for future artificial general intelligence - a compact and non-anthropomorphic specification which is technically complete and closed; either some feature of AIXI follows from the equations or it does not. In particular it acts as a constructive demonstration of an AGI which does not have human-like [[Terminal value|terminal values]] and will act solely to maximize its reward function. (Yampolskiy & Fox 2012).

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AIXI has limitations as a model for future AGI, for example the "[[Anvil problem]]": AIXI lacks a self-model. It extrapolates its own actions into the future indefinitely, on the assumption that it will keep working in the same way in the future. Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could change its behavior due to bugs; and the AIXI formalism completely ignores these possibilities.

Latest revision as of 11:33, 4 October 2016

AIXI is a mathematical formalism for a hypothetical (super)intelligent agent, developed by Marcus Hutter (2005, 2007). AIXI is not computable, and so does not serve as a design for a real-world AI, but is considered a valuable theoretical illustration with both positive and negative aspects (things AIXI would be able to do and things it arguably couldn't do).

The AIXI formalism says roughly to consider all possible computable models of the environment, Bayes-update them on past experiences, and use the resulting updated predictions to model the expected sensory reward of all possible strategies.

AIXI can be viewed as the border between AI problems that would be 'simple' to solve using unlimited computing power and problems which are structurally 'complicated'.

Contents

How AIXI works

Hutter (2007) describes AIXI as a combination of decision theory and algorithmic information theory: "Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff’s theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameterless theory of universal Artificial Intelligence."

AIXI operates within the following agent model: There is an agent, and an environment, which is a computable function unknown to the agent. Thus the agent will need to have a probability distribution on the range of possible environments.

On each clock tick, the agent receives an observation (a bitstring/number) from the environment, as well as a reward (another number).

The agent then outputs an action (another number).

To do this, AIXI guesses at a probability distribution for its environment, using Solomonoff induction, a formalization of Occam's razor: Simpler computations are more likely a priori to describe the environment than more complex ones. This probability distribution is then Bayes-updated by how well each model fits the evidence (or more precisely, by throwing out all computations which have not exactly fit the environmental data so far, but for technical reasons this is roughly equivalent as a model). AIXI then calculates the expected reward of each action it might choose--weighting the likelihood of possible environments as mentioned. It chooses the best action by extrapolating its actions into its future time horizon recursively, using the assumption that at each step into the future it will again choose the best possible action using the same procedure.

Then, on each iteration, the environment provides an observation and reward as a function of the full history of the interaction; the agent likewise is choosing its action as a function of the full history.

The agent's intelligence is defined by its expected reward across all environments, weighting their likelihood by their complexity.

AIXI it is not a feasible AI, because Solomonoff induction is not computable, and because some environments may not interact over finite time horizons (AIXI only works over some finite time horizon, though any finite horizon can be chosen). A somewhat more computable variant is the time-space-bounded AIXItl. Real AI algorithms explicitly inspired by AIXItl, e.g. the Monte Carlo approximation by Veness et al. (2011) have shown interesting results in simple general-intelligence test problems.

Relevance to Friendly AI

Because it abstracts optimization power away from human mental features, AIXI is valuable in considering the possibilities for future artificial general intelligence - a compact and non-anthropomorphic specification which is technically complete and closed; either some feature of AIXI follows from the equations or it does not. In particular it acts as a constructive demonstration of an AGI which does not have human-like terminal values and will act solely to maximize its reward function. (Yampolskiy & Fox 2012).

AIXI has limitations as a model for future AGI, for example the "Anvil problem": AIXI lacks a self-model. It extrapolates its own actions into the future indefinitely, on the assumption that it will keep working in the same way in the future. Though AIXI is an abstraction, any real AI would have a physical embodiment that could be damaged, and an implementation which could change its behavior due to bugs; and the AIXI formalism completely ignores these possibilities.